Is there an option for using a Display name or number as a Match Condition for Triggers?

This would be very useful for example to separate and identify a specific browser window when there are several browser windows present on different displays.

Yes. Exactly that.
If you want to target an application like a browser, where you have several different windows on different monitors, there is no way to target a specific one, as they all share the same process name and windows class, and the window text changes with every tab inside each window.

Thanks. Having several browser windows across different displays is something that many people do in daily work.